1. RESEARCH AND INTERNALIZATION across DEPARTMENTS

2. Faculty of Law and Administration Major studies and research projects Europeanisation of Law Naturalization of Law Barriers towards EU citizenship Restorative Justice and Mediation Collaboration Faculty scholars are members of international expert groups in organisations such as the European Labour Law Network, the International Committee of the Red Cross, and the international forum for environmental protection of the Avosetta Group, and the Acquis Group. Regular scientific cooperation takes place between the University of Augsburg (Krakauer- Augsburger Rechtsstudien), Harvard University (Harvard Negotiation Project), the University of Wrocław (The Kraków-Wrocław Scientific Meeting of Administrators), and the University of Greifswald (projects include Mare Balticum – Strafvollzug und die Beachtung der Menschenrechte, Comparative Analysis of Women's Prisons: Current Situation, Demand Analysis, and Best Practice, andLong-term Imprisonment and Human Rights, Juvenile Justice Systems in Europe).

3. Faculty of Medicine Major studies and research projects The Development of Individualised Medicine New Lines of Research in Various Medical Fields Collaboration The Faculty of Medicine participates in a joint initiative of KNOW (Leading National Research Centre) with the Institute of Pharmacology of the Polish Academy Of Sciences in Kraków and co- creates a scientific consortium with the Faculty of Chemistry at Jagiellonian University which offers Mol-Med doctoral studies. Studies on differential diagnostics of diabetes types, evaluation of the quality of ageing populations as well as health determinants and life quality of the elderly are conducted in partnership with scientific centres from the United States, Great Britain, Germany, Sweden, Belgium and Spain. This collaboration also involves research on new endocrine peptides and radiopharmaceuticals, as well as on the genetic background of hypertension and organ damage due to this disease.

4. Faculty of Pharmacy Major studies and research projects Neuropathic Pain and/or Epilepsy: Towards New Drugs In Vitro Cultures of Medicinal Plants and Fungi Modern Drug Forms: Biopharmaceutical Aspects Sensitization and Toxicity of Drugs' and Cosmetics' Ingredients New Drug in the Treatment of Central Nervous System Collaboration Research projects are carried out in collaboration with numerous international centres, such as the National Institutes of Health and the National Cancer Institute of the United States as well as pharmaceutical faculties and research institutes from France, Germany, Israel, the United Kingdom, Italy, Turkey, Finland, Portugal, and Canada. In relation to the conducted research, scientists at the Faculty work with Adamed, Apipol, Farmina, and other pharmaceutical companies in Poland.

5. Faculty of Health Sciences Major studies and research projects Cardiovascular Disease Prevention: Efficiency Control Economic and Psychosocial Factors and Health Status Factors Affecting the Levels of Female Sex Hormones Changes in Dietary Habits Organisation of the Employment of Nursing Personnel Collaboration Scientists from the Faculty of Health Sciences participate in research projects conducted by scientific consortia (e.g. the 7PR UE Eatwell Consortium and UE CHANCES – Consortium on Health and Ageing: Network of Cohorts in Europe and the United States). They also collaborate with the following universities and research centres: the University of Texas; the Health Science Center San Antonio; the Department of Cellular and Structural Biology; the Artificial Limb Centre (CRA – Centre de Rééducation et d'Appareillage) of Institut Robert Merle d'Aubigne, Valenton (France); Harvard University; the University of Tromsø; Katholieke Uniwersiteit Leuven (Belgium); the University of Kuopio (Finland); Technische Universitat Berlin; and many others.

6. Faculty of Philosophy Major studies and research projects Psychology Sociology Philosophy Religious Studies Cultural Studies Pedagogy Collaboration Scholars from the Faculty of Philosophy of the Jagiellonian University are involved in several dozen international projects, e.g. one concerning gender equality, which brings together researchers from Oslo and Kraków. Research devoted to the cultures of ancient Mexico is conducted in collaboration with the Instituto Nacional de Antropología e Historia, while academics from the Institute of Psychology collaborate with the University of Maryland (studies on motivated social cognition), Pennsylvania State University (studies on bilingualism), and the Université Libre de Bruxelles (studies on consciousness)

7. Faculty of History Major studies and research projects Sacred Art. Archaeological Studies Searching for Polonica in Foreign Libraries Studies in Antiquity Collaboration Collaboration in the Union Academique Internationale is worth mentioning as one of several dozen international research projects in which scholars from the Jagiellonian University Faculty of History participate. The projects include: Corpus Antiquitatum Americansium and Carte de Monde Inca. They encompass publishing the findings of archaeological studies carried out in the Peruvian Andes and Argentina. Thanks to collaboration with the Fulbright program (United States) and the Anthropos Institute in Sankt Augustin (Germany), the Institute of Ethnology and Cultural Anthropology frequently hosts foreign visitors from the United States, Great Britain, Germany, and Denmark, etc. Domestic partners include the German Historical Institute in Warsaw, the Shalom Foundation, and the Auschwitz-Birkenau State Museum.

8. Faculty of Philology Major studies and research projects Teaching Intercultural Communication Translation Studies on a Collection of Romance-language Manuscripts Philological Studies on Greek Religion Roots of European Culture Studies in Kurdish Culture Collaboration A notable example of scholarly cooperation with foreign partners is the international research project entitled Traduction comme moyen de communication interculturelle, where researchers from the Institute of Romance Studies work together with colleagues from Université Charles-de Gaulle-Lille 3 and Université de Mulhouse. Scholars from the Faculty of Philology are also partners in the research project Western- Eastern Europe: Centre-Periphery Dynamics, whose objective is an interdisciplinary study of the topic of centre and periphery in modern culture. Another example of a fruitful academic collaboration is the international conference Points of View in Language and Culture – Audiovisual Translationorganised by the Faculty. Guest lectures offered in many foreign universities by Dr Piotr Tylus from the Institute of Romance Studies cannot be omitted in this section. He has been invited to speak at the Sorbonne (Paris 3), Université de Paris XIII, and Université de Versailles-Saint-Quentin-en-Yvelines. Piotr Tylus maintains regular scientific contact with the international community of medievalists including professors from the College de France, the Sorbonne, and many others.

9. Faculty of Polish Studies Major studies and research projects Cultural Literary Theory Comparative Studies Historical and Literary Studies Editorial Studies Drama and Theatre Studies Linguistic Studies Collaboration World-famous image and media culture researchers (William J. T. Mitchell from the University of Chicago), literary philosophers (Rodolphe Gasché from State University of New York, Buffalo), and historians of ideas (Martin Jay from the University of California, Berkeley) have collaborated with the faculty. Scholars from the Faculty of Polish Studies are involved in numerous national and international research projects, and they belong to consortia whose members come from excellent universities in Europe, Asia, Australia, North America and South America, e.g. Interzones and SPeCTReSS. The faculty has a full teaching module in English and its academic staff includes visiting professors from abroad (e.g. the United States).

10. Faculty of Physics, Astronomy and Applied Computer Science Major studies and research projects Processes occurring in the Universe Intelligent computer systems and their applications FAIR (Facility for Antiproton and Ion Research in Europe) Research on the fundamental interactions Collaboration The participation of Faculty scientists in the BOREXINO (Boron Solar Neutrino Experiment) project is an example of broad international collaboration. During the realisation of the project, scientists obtained direct confirmation of the occurrence of geoneutrinos. It also allowed for the most precise measurement of the velocity of neutrinos emitted at CERN. The acquired results are of fundamental importance for astrophysics, particle physics and geophysics. Another enterprise of this kind is research conducted by means of the LOFAR (Low Frequency Array) equipment / radiotelescopes. It concerns the physics of the Earth's ionosphere, interstellar plasma, neutron stars and galactic nuclei. Other research that deserves attention is conducted within the Polish part of the consortium for the Cherenkov Telescope Array (CTA) project, which concerns high-energy cosmic ray particles that were produced as a result of stellar explosions, generated inside galactic nuclei, or remained from the early Universe.

11. Faculty of Mathematics and Computer Science Major studies and research projects Functional Analysis Complex Analysis Algebraic Geometry Analytical Computer Science Computational Mathematics Collaboration Research in mathematical sciences has a more individual character than in other scientific fields; thus, collaboration with other centres is rarely of an institutional nature. Proof of a lively exchange between scholars from the faculty and the world's leading scientists are the papers written in collaboration with mathematicians, physicists and computer scientists from top (according to the world rankings) universities, including Princeton, Paris 6, Texas A&M, Georgia Institute of Technology, Rutgers, Tel Aviv, Colorado, Paris 7, Pennsylvania, Toronto, Illinois, TU Berlin, Vanderbilt, Hannover, and many others, as well as numerous visits by computer scientists and mathematicians from the faculty at leading universities

12. Faculty of Chemistry Major studies and research projects New Materials Borderlands of Chemistry and Biochemistry Studies Organic chemistry Materials for Clean Technologies Catalysis Collaboration Research teams from the Faculty collaborate with national and international institutions: universities, the institutes from the Polish Academy of Sciences, other research institutes, and chemical industry partners (e.g. LOTOS Oil, SK Innovation Co. from South Korea, and Scientific Computing & Modeling from the Netherlands). Together with four other scientific institutions, the faculty created the KNOW Matter-Energy-Future Consortium. Within the ERA-Chemistry network, under the EU Open Initiative 2008programme, the faculty has an ongoing cooperation with the University of Coimbra in the area of photosensitizers for applications in photocatalysis, medicine, optoelectronics, and solar energy conversion. The faculty has its representatives on the Steering Committee of the European network of Precision Polymer Materials.

13. Faculty of Biology and Earth Sciences Major studies and research projects Studies on Life Strategies of Organisms in Various Environmental Conditions Genetic and Biochemical Diversity Ecosystem Functioning Cellular, Developmental, and Reproductive Biology Neurobiology and Immunobiology Anthropogeography Physical Geography Paleoenvironmental Analysis and Geochemistry Tectonics and Sedimentology Collaboration National and international cooperation result in research projects, PhD studies, scientific achievements, and numerous publications in prestigious journals. For example, the possibility of using antiepileptic drugs in support of chemotherapy is explored in collaboration with the Department of Neurology at Oslo University Hospital (Norway). Researchers from the faculty send data to the international journal Atlas Florae Europaeae, which presents the distribution of plants in Europe (sixteen volumes published), and to the global data network GBIF (Global Biodiversity Information Facility). The faculty has also made a significant contribution to the development of the international scientific network Science for the Carpathians (S4C), which promotes interdisciplinary research about the Carpathians.

14. Faculty of Management and Social Communication Major studies and research projects Entrepreneurship in Sport and Tourism Mass Media vs. Participation of Citizens and Public Political Discourse Pedagogical Supervision Internet Knowledge Resources Sleep Deficiency: Brain Bioelectric Activity New Study on the History of World Cinema Collaboration In a framework of cooperation between IBM and the Complex Systems Modelling Workshop in the Institute of Applied Psychology, analytical solutions are used that serve building prediction models, forecasting, and simulation of phenomena on the bases of complex data. The Workshop is included in the IBM Academic Initiative (2012–2017) under which student internships are implemented and access to software and training materials is possible. From 2007 to 2010, the research project LLP: School and World of Work was conducted at the Institute of Economics and Management. Together with representatives of twelve EU member states work began on creating the largest European network of employers and contacts of secondary and higher education establishments – a system that would limit graduate unemployment as well as support their mobility. Other Faculty institutes also carry out various scientific and educational activities based on multilateral cooperation with other centres.

15. Faculty of International and Political Studies Major studies and research projects Political Theories, Systems and Thought Public Order, Security and Communication Countries, Nations and Civilisations Collaboration Faculty scholars participate in numerous international projects and are members of the Association of European Migration Institutions and Academia Europaea. They participate in conferences organised alternately in Kraków and Moscow with scholars from Lomonosov Moscow State University. Faculty scholars also participate in symposia of the Polish Society of Political Science, the Polish Academy of Arts and Sciences, the International Political Science (IPSA), the International Studies Association (ISA), the Central and Eastern European International Studies Association (CEEISA), and the Standing Group on International Relations (SGIR). Guest lectures are conducted each year by recognised academics from abroad. In addition, courses are taught by visiting professors from various countries.

16. Faculty of Biochemistry, Biophysics and Biotechnology Major studies and research projects Biochemistry and Molecular Biology Biophysics Microbiology, Virology and Immunology Collaboration The Faculty conducts fruitful scientific collaboration with more than 80 Polish and international academic centres. These partnerships carry out joint research, provide for student and academic staff exchange, and have implemented multilateral education programmes leading to a dual diploma. Two centres with which the Faculty has collaborated for an extended period include Lund University (Sweden) and Medical College of Wisconsin (United States). The Faculty frequently organises international scientific conferences (e.g. International Workshop on EPR in Biology and Medicine).

17. Jagiellonian Library Major studies and research projects Creating Catalogues Studies on Hebrew Manucripts Texts on Medieval University of Kraków Manuscript Heritage after Michał Pawlikowski (1887–1970) Orientalia Polonica Series Collaboration Scholars of the Jagiellonian Library arranged and made available significant material kept in the Polish Library in Paris which concerns the history of the Polish Diaspora in France. This research resulted in the publication of the volume entitled Archiwum Zygmunta Lubicz Zaleskiego w zbiorach Biblioteki Polskiej w Paryżu (The archives of Zygmunt Lubicz Zaleski in the collections of the Polish Library in Paris; Kraków 2011). The next stage of the collaboration with the Polish Library in Paris aims at examining the priceless collection of documents concerning the life of Polish Diaspora in 19th-century France. The Jagiellonian Library has conducted this project in cooperation with the Polish Academy of Arts and Sciences and the Faculty of History of the Jagiellonian University.

18. Copernicus Center for Interdisciplinary Studies Major studies and research projects Philosophy of Science in European Perspective The Limits of Scientific Explanation Collaboration The Copernicus Center, as a joint venture between the Jagiellonian University and the Pontifical University of John Paul II, associates not only eminent scientists from both universities, but scholars from other scientific institutions in Poland (e.g. the Polish Academy of Sciences, the Polish Academy of Arts and Science, AGH University of Science and Technology, the University of Social Sciences and Humanities, and Warsaw University of Technology), and abroad (the University of Michigan, the University of Bologna, Catholic University of Leuven, and the University of Namur).

19. Jagiellonian Centre for Experimental Therapeutics Major studies and research projects Endothelium in Civilisation Diseases Endothelium and Cancer Pharmacology of Carbon Monoxide-Releasing Compounds Collaboration JCET's activity is based on extensive domestic and international cooperation, particularly in the field of medical chemistry and the development of original chemical structures acting on endothelium. The list of JCET's significant foreign partners includes the Institute of Organic Synthesis (Latvia), National Institute of Health (United States), University of Zurich (Switzerland), University of Exeter (United Kingdom), and Universite Paris-Est (France). Domestic partners include the Łódź University of Technology, Poznań University of Technology and the Institute of Biotechnology and Antibiotics in Warsaw. Scientists from JCET collaborate within the framework of research on endothelium and cancers with four institutions in Poland: the Institute of Immunology and Experimental Therapy of the Polish Academy of Sciences in Wrocław, the Medical University of Gdańsk, the Medical University of Białystok, and the Medical University of Łodź, as well as with foreign partners such as the aforementioned Institute of Organic Synthesis in Riga. In the scope of the research project Endothelium in Civilisation Diseases... JCET collaborates with a total of seventeen research teams from nine scientific centres in Poland.

20. Małopolska Centre of Biotechnology Major studies and research projects Light – Circadian Rhythm – Retinal Degeneration Studies on Epithelium Potential Anticancer Drugs Treatment of chronic obturative pulmonary disease Collaboration Scientists from the Malopolska Centre of Biotechnology collaborate with various domestic and international research centres. The Malopolska Centre of Biotechnology signed cooperation agreements with Max Planck Gesellschaft in Germany (the research team is formed by MPG at MCB), Centre National de la Recherche Scientifique in France (the agreement allows for the financing of research at MCB laboratory), Kyoto University in Japan, and the National Institute of Agrobiological Sciences (NIAS) Tsukuba in Japan. Negotiations are in progress for a cooperation agreement with Oxford University.

21. SOLARIS National Synchrotron Radiation Centre Major studies and research projects PLGrid Plus Swiss Light Source Performance Improvement Project Liquid Crystals Studies DYNASYNC Collaboration The Synchrotron Radiation Centre works closely with international synchrotron centres, such as MAX IV Laboratory (Sweden), Elettra (Italy), CELLS – ALBA Synchrotron (Spain), and Swiss Light Source (Switzerland). Synchrotron Centre MAX IV Laboratory at Lund University (Sweden) is a strategic partner for the SOLARIS team. It carries out one of the most advanced projects in the world: the construction of two synchrotrons and a free-electron laser. This cooperation allowed for this expertise and know-how to be used in the construction of the Polish synchrotron, which will be a replica of the Swedish synchrotron. Scientists at the Centre, together with the Jerzy Haber Institute of Catalysis and Surface Chemistry at the Polish Academy of Sciences, collaborate with the Swiss Paul Scherrer Institut (PSI) and conduct final tests of the experimental station for the Polish synchrotron. At each stage of the synchrotron's construction, scientists from SOLARIS collaborate with the Polish Synchrotron National Consortium, which includes representatives from 36 universities and research institutes in Poland. A similar cooperation is carried out in consultation with the Polish Synchrotron Radiation Society (PTPS), involving more than 150 scholars.

22. Centre for Technology Transfer CITTRU Major studies and research projects Technological Offer of the Jagiellonian University "On Request" Research Offer Collaboration of Scholars with Economic Environment Collaboration A key activity of CITTRU is identifying and starting business cooperation with companies: prospective buyers of innovations developed at the Jagiellonian University and clients of research services. Every year, CITTRU establishes cooperation with various national and international companies (e.g. Simcyp from Great Britain, and Unilab from the United States) regarding selling rights to discoveries made by the Jagiellonian University scholars or funding further research aimed at increasing the functionality of the discovery (implementation work). Moreover, CITTRU initiates industry meetings with business representatives in various countries and with international organisations that promote the cooperation of science with business (e.g. ASTP Proton). In creating scientific consortia with business (e.g. the US-based Unilab Inc.), it is important for this unit of the Jagiellonian University to be active, as it allows joint research and development projects to be implemented as well as to optimise developed "scientific products" to fit the needs of the market.

23. RESEARCH AND INTERNALIZATION across DEPARTMENTS examples

24. The Kurds – how to make a voice audible? FACULTY OF PHILOLOGY, INSTITUTE OF ORIENTAL STUDIES Research team: Joanna Bocheńska, PhD, Institute of Oriental Studies – Project Manager; Renata Kurpiewska-Korbut, PhD, Institute of the Middle and Far East; Marcin Rzepka, PhD, Institute of History, The Pontifical University of John Paul II in Kraków; Krzysztof Lalik, PhD student, Institute of the Middle and Far East Bookshop in Hawlêr (Erbil), South Kurdistan. Photo: Joanna Bocheńska The Kurds are one of the larger nations, with 40 million people. They inhabit a region that currently belongs to the territory of four countries: Turkey, Iraq, Syria and Iran. Kurdish independence movements have always attracted special attention to the problem of their national identity. More complex approach of JU researchers – not limited to question of national identity Knowledge of Kurdish language is the basis of the research carried out at the Section for Kurdish Studies that was created in 2008 at the Department of Iranian Studies at the Institute of Oriental Studies. Classical and contemporary Kurdish literature became the starting point for the project. The relations between the Kurds and other minorities Systematization of knowledge about Kurdish culture, contemporary reality of Kurdistan, and the situation of Kurds inhabiting Europe. Studies that are based on the analysis of Kurdish art and interviews with people who are responsible for the implementation of Kurdish cultural policy or with representatives of Christian minority groups. Development of international co-operation, obtaining content- related support of experienced research units and most of all, inviting Kurdish scientists and intellectuals to cooperate. The project may also enable the Jagiellonian University to become an important center of Kurdish studies that will attract the Kurdish diaspora dispersed throughout Europe in the near future. Centre for Kurdish Studies: www.kurdishstudies.pl.www.kurdishstudies.pl.

25. How to manage a city? FACULTY OF INTERNATIONAL AND POLITICAL STUDIES, INSTITUTE of EUROPEAN STUDIES Research conducted by: Katarzyna Romańczyk, PhD — Project Manager Analyzing how municipal authorities are managing the city of Brussels, a relatively small urban center where the needs of inhabitants have been pushed into the background for years by the interests of international institutions. Main aim of these studies is to analyze good practices and to determine the most effective tools of municipal policy. Brussels: Social and spatial fragmentation, a high level of unemployment (22% in 2013), suburbanization, and difficulties with the adaptation of immigrants make Brussels a city full of paradoxes. Due to the political divisions between the Flemish and the Walloons, sometimes many municipal institutions in Brussels either work together or parallel to each other, and sometimes even against one another. What form of urban governance might seem to meet the expectations of residents in these conditions? Neighborhood contracts are an example of a good practice in this area. Neighborhood contracts attract the attention of the local community and create a kind of forum for its activity. Neighborhood contracts are programs containing an action plan concerning selected areas of the city. Projects accepted under these contracts are defined and realized with the participation of inhabitants. They refer to the closest environment of residents, including the improvement of road infrastructure, quality of public spaces, housing conditions, the development of social and cultural activities, and, finally, environmental protection. Similar practices have already been introduced, with varied effects, in Poland

26. Scare away the demons of fear FACULTY OF PHILOSOPHY, INSTITUTE OF PEDAGOGY Research team: Jacek Bylica, PhD, Institute of Pedagogy at the Jagiellonian University in Kraków; Barbara Surzyn, MA, psychologist at the Social Welfare Centre in Andrychów; Zoran Bikovski and Zekir Abdulov, NGO KHAM Delcevo, Macedonia Analyzing how municipal authorities are managing the city of Brussels, a relatively small urban center where the needs of inhabitants have been pushed into the background for years by the interests of international institutions. Main aim of these studies is to analyze good practices and to determine the most effective tools of municipal policy. Joint Polish-Macedonian project of significant social importance Not limited to academic environment but with active participation of social and NGO workers Employees of public institutions and NGOs whose task is to contact the Romani minority should have appropriate qualifications. Problems affecting most of the Romani in Poland and in Europe, such as unemployment, poverty, and social exclusion, are connected with a very low level of education. This in turn results from the Romani's lack of trust in non-Romani forms of upbringing, as they follow their own code of conduct called the Romanipen. Since people tend to evaluate others from the point of view of their own value systems, this approach is met with disapproval from most Europeans. Research and training project which not only enabled the analysis and development of the knowledge and skills of the people responsible for good relations with the Romani community in the Nowy Sącz region, but also allowed for the preparation of research tools to measure these competences. Approach combining theory and practice called participatory action research. This enabled the subjects to become participants and partners, and the study itself became practice as it led to solving problems similar to those faced by the participants in their work. Józef Orłowski, President of Malopolska and the Silesian Roma Association, Poland. Photo by Andrzej Grzymała – Kazłowski Ethnographic empathy approach, which allows for a better understanding of the Romani world. As a consequence, it leads to the application of the empowerment strategy, which is the method of activating the cultural potential of Romani communities instead of imposing ready-made external solutions on them (which is usually done without Romani participation in the decision-making process. Measurement of intercultural competences of representatives of several NGOs in Skopje, Macedonia, conducted in October 2012. The measurement was carried out with the use of interviews and the Questionnaire of Romani Intercultural Competences, along with an evaluation of the nature of social policy that has been implemented towards Macedonian Roma. The Republic of Macedonia is one of the signatories of the Decade of Roma Inclusion in Europe. The nongovernmental sector actively participates in the implementation of specific tasks of the Decade.

27. Space laboratory of plasma physics FACULTY OF PHYSICS, ASTRONOMY AND APPLIED COMPUTER SCIENCE Research team: Krzysztof Chyży, PhD; Robert Drzazga, MSc; Wojciech Jurusik, MSc; Professor Marek Urbanik; Marian Soida, PhD; Jacek Knapik, MSc; Błażej Nikiel-Wroczyński, MSc; Professor Katarzyna Otmianowska–Mazur; Natalia Nowak, MSc Apart from the commonly known states of matter: liquid, solid and gas, physicists distinguish one more, a fourth state called plasma. This kind of matter has an increasing number of applications in modern technology. It is used, among others, in television or computer screens and the rocket engines of the future. This is why research on plasma is one of the essential fields in modern physics. Outer space as a laboratory for plasma research The properties of plasma are analyzed using its magnetism Analyzing plasma properties with use of radio telescopes across the galaxy, revealing the structure of the magnetic lines. Studying such exotic objects as galaxies, we managed to collect a wide database concerning various properties of magnetized plasma in conditions unattainable in laboratories on Earth. This is a valuable supplement to our knowledge about the physics of plasma Scientists from Kraków, using a network of antennas in the United States, discovered ordered magnetic fields in a galaxy group called Stephan's Quintet. Rare example of applied approach in the astrophysics

28. Mathematical forecasting of the future FACULTY OF MATHEMATICS AND COMPUTER SCIENCES Research team: Paweł Dłotko, PhD; Marc Ethier, PhD; Paweł Gniadek, PhD; Mateusz Juda, PhD; Tomasz Kapela, PhD; Małgorzata Moczurad, PhD; Professor Marian Mrozek; Daniel Wilczak, PhD; Professor Piotr Zgliczyński; Marcin Żelawski, PhD; Piotr Brendel, MSc; Aleksander Czechowski, MSc; Grzegorz Jabłoński, MSc; Piotr Kamieński, MSc; Łukasz Piękoś, MSc; Piotr Rytko, MSc; Robert Szczelina, MSc; Hubert Wagner, MSc; Irmina Walawska, MSc; Frank Weilandt, MSc Major research partners: the Institute of Science and Technology, Austria and Rutgers University, New Jersey, USA. Advanced mathematical studies are related, among other things, to forecasting the future. Contrary to algebraic equations from school, the solution of a differential equation is not a number, but a function describing the course of a given physical process in time. Additionally, there are an infinite number of solutions. In order to select one specific solution, the value of the function at a given moment is set. A tool which enabled the accurate estimation of rounding in numerical analysis, so-called interval arithmetic, was developed in the mid-twentieth century by Polish mathematician Mieczyslaw Warmus and, at the same time, by the American scientist Ramon E. Moore. Scientists have succeeded in developing a CAPD library consisting of over 60,000 lines of code, which is used for rigorous numerical analysis of differential equations, and a sub-library CAPD::REDHOM, which encompasses the implementation of topological algorithms. The library contains computer programs that enable the practical application of the discussed methods. It is successfully used by numerous scientists, both in Poland and throughout the world Visualization of the differential equations discovered by Lorenz. It demonstrates the sensitive dependence of solutions on initial conditions, so-called deterministic chaos